Comparing Two Numbers

Comparing Two Numbers

When comparing two numbers, $x$ and $y$, there are three possibilities:

• $x = y$
• x < y (x is less than y. The less than symbol points to the left.)
• x > y (x is greater than y. The greater than symbol points to the right.)

Examples

• Comparing 3 and 5: 3 < 5
• Comparing 100 and 28: 100 > 28

Comparing Decimals

• Start at the left and compare digits in the same place value.
• Adding zeros to the end of the shorter decimal can be helpful to make comparison easier without changing the number's value. For example, $0.05 = 0.050 = 0.0500$

Examples with Decimals

1. Comparing $0.025$ and $0.25$
   • In the tenths place, $0.025$ has a 0, while $0.25$ has a 2. Since 0 < 2, 0.025 < 0.25. Adding a zero to the end of $0.25$ to make it $0.250$ can make the comparison easier.
2. Comparing $2.875$ and $2.785$
   • In the tenths place, $2.875$ has an 8, while $2.785$ has a 7. Since 8 > 7, 2.875 > 2.785.

Comparing Negative Numbers

• On the number line, the further left a number is, the smaller it is.
• The negative side of the number line goes backward, meaning the further you get in the negative direction, the smaller you are.
• Example: Comparing -9 and -2: -9 < -2

Additional Examples

1. Comparing $0.75$ and $0.749$
   • They differ in the hundredths place. Since 5 > 4, 0.75 > 0.749. Adding a zero to the end of $0.75$ to make it $0.750$ can make the comparison easier.
2. Comparing $0.05$ and $0.050$
   • Adding a zero to the end of a decimal doesn't change its value, so $0.05 = 0.050$.
3. Comparing $3.14$ and $3.141$
   • Adding a zero to the end of $3.14$ to make it $3.140$ can make the comparison easier. Since 0 < 1, 3.14 < 3.141.

Importance in Statistics

Accurately comparing two decimals is a very important skill to have for statistics.